Explanation Given: There are 4 vertices and 5 directed edges. Calculation: Every vertex is connected to other vertex through arrows. Start from vertex 1, the walk can be made towards three other vertices that are 2, 3 and 4, thus the probabilities for the walk from vertex 1 towards 2, 3 and 4 is 1 3 each. From vertex 2, the walk can be made towards another vertex that is 4, thus the probability for the walk from vertex 2 towards 4 is 1. From vertex 3, the walk can be made towards another vertex that is 1, thus the probability for the walk from vertex 3 towards 1 is 1. From vertex 4, the walk can be made towards two other vertices that are 2 and 3, thus the probabilities for the walk from vertex 4 towards 2 and 3 is 1 2 each. Based upon above computation, obtain the transition matrix P for the simple random walk as follows. P = [ 0 0 1 0 1 3 0 0 1 2 1 3 0 0 1 2 1 3 1 0 0 ] Consider the initial probability vector as x 0 = [ 1 0 0 0 ] Compute the value of x 1 with the help of x 1 = P x 0 as follows, x 1 = P x 0 = [ 0 0 1 0 1 3 0 0 1 2 1 3 0 0 1 2 1 3 1 0 0 ] × [ 1 0 0 0 ] = [ 0 1 3 1 3 1 3 ] That is, x 1 = [ 0 1 3 1 3 1 3 ]

Linear Algebra and Its Applications (5th Edition)

5th Edition

ISBN: 9780321982384

Author: David C. Lay, Steven R. Lay, Judi J. McDonald

Publisher: PEARSON

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Chapter 10.1, Problem 25E

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Chapter 10.1, Problem 24E

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Chapter 10 Solutions

Linear Algebra and Its Applications (5th Edition)

Ch. 10.1 - Fill in the missing entries in the stochastic...Ch. 10.1 - Prob. 2PP Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - In Exercises 5 and 6, the transition matrix P for...Ch. 10.1 - Prob. 6E Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...

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Chapter 10 Solutions